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S is the product of a list of consecutive integers from 1 to

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Intern
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S is the product of a list of consecutive integers from 1 to [#permalink] New post 15 Jun 2006, 14:20
S is the product of a list of consecutive integers from 1 to 24, and 10k is a factor of S. What is the largest k?

A. 1
B. 2
C. 3
D. 4
E. 5

Answer is D. WHY?
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 [#permalink] New post 15 Jun 2006, 14:42
I am stumped... what is 10K? Is it 10xk or is k the unit's digit of the number 10k?

Do you mean 10^k

If it is 10^k, then the answer D makes sense and here's how.

S= 1x2x3x4x5....x24
= 2x5x10x15x20x (prod of the rest)
= 10 x 10 x 5x3 x 5x4 x P
= 10 x 10 x 10 x 10 x 3xP
= 10^4 xP'

Therefore k max value is 4.
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 [#permalink] New post 15 Jun 2006, 14:55
haas_mba07 wrote:
I am stumped... what is 10K? Is it 10xk or is k the unit's digit of the number 10k?

Do you mean 10^k

If it is 10^k, then the answer D makes sense and here's how.

S= 1x2x3x4x5....x24
= 2x5x10x15x20x (prod of the rest)
= 10 x 10 x 5x3 x 5x4 x P
= 10 x 10 x 10 x 10 x 3xP
= 10^4 xP'

Therefore k max value is 4.


Yea this approach is right, you just need to collect all the 2x5 and see how many 10s you get in the product
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 [#permalink] New post 16 Jun 2006, 00:06
Yep. Assuming 10^k, answer is 4. Find the number of 5s.
  [#permalink] 16 Jun 2006, 00:06
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